LMFDB - Embedded newform 9016.2.a.bo.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9016,2,Mod(1,9016)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9016, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("9016.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 9016 = 2^{3} \cdot 7^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9016.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$71.9931224624$
Analytic rank:	$1$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - 2 x^{10} - 20 x^{9} + 37 x^{8} + 125 x^{7} - 215 x^{6} - 278 x^{5} + 443 x^{4} + 256 x^{3} + \cdots + 99 $ x^11 - 2x^10 - 20x^9 + 37x^8 + 125x^7 - 215x^6 - 278x^5 + 443x^4 + 256x^3 - 362x^2 - 85x + 99
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 1288)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-0.852282$ of defining polynomial
Character	$\chi$	$=$	9016.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.852282 q^{3} -1.25440 q^{5} -2.27361 q^{9} +O(q^{10})$	$q-0.852282 q^{3} -1.25440 q^{5} -2.27361 q^{9} +5.69315 q^{11} +1.56428 q^{13} +1.06910 q^{15} +3.66751 q^{17} -5.11241 q^{19} -1.00000 q^{23} -3.42649 q^{25} +4.49461 q^{27} -3.12094 q^{29} -1.41394 q^{31} -4.85217 q^{33} +1.30698 q^{37} -1.33321 q^{39} +2.24298 q^{41} -5.84516 q^{43} +2.85201 q^{45} -4.61410 q^{47} -3.12575 q^{51} +8.59490 q^{53} -7.14147 q^{55} +4.35722 q^{57} -12.9000 q^{59} -5.04838 q^{61} -1.96222 q^{65} +12.7962 q^{67} +0.852282 q^{69} +12.6302 q^{71} -9.46838 q^{73} +2.92034 q^{75} +6.31953 q^{79} +2.99017 q^{81} -11.3499 q^{83} -4.60051 q^{85} +2.65992 q^{87} -1.76876 q^{89} +1.20507 q^{93} +6.41299 q^{95} +6.92877 q^{97} -12.9440 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q + 2 q^{3} - 9 q^{5} + 11 q^{9}+O(q^{10}) $ 11 * q + 2 * q^3 - 9 * q^5 + 11 * q^9	$ 11 q + 2 q^{3} - 9 q^{5} + 11 q^{9} - 15 q^{13} - 2 q^{15} - 5 q^{17} - 11 q^{23} + 22 q^{25} + 5 q^{27} + 5 q^{29} - 6 q^{31} - 14 q^{33} - q^{37} + 11 q^{39} - 20 q^{41} - 7 q^{43} - 41 q^{45} + 3 q^{47} - 13 q^{51} + 19 q^{53} + 3 q^{55} - 5 q^{57} - 7 q^{59} - 39 q^{61} + 5 q^{65} + 7 q^{67} - 2 q^{69} - 19 q^{71} + 5 q^{73} - 16 q^{75} + 11 q^{79} + 43 q^{81} - 33 q^{83} - 13 q^{85} + 30 q^{87} - 34 q^{89} - 12 q^{93} + 37 q^{95} - 17 q^{97} - 49 q^{99}+O(q^{100}) $ 11 * q + 2 * q^3 - 9 * q^5 + 11 * q^9 - 15 * q^13 - 2 * q^15 - 5 * q^17 - 11 * q^23 + 22 * q^25 + 5 * q^27 + 5 * q^29 - 6 * q^31 - 14 * q^33 - q^37 + 11 * q^39 - 20 * q^41 - 7 * q^43 - 41 * q^45 + 3 * q^47 - 13 * q^51 + 19 * q^53 + 3 * q^55 - 5 * q^57 - 7 * q^59 - 39 * q^61 + 5 * q^65 + 7 * q^67 - 2 * q^69 - 19 * q^71 + 5 * q^73 - 16 * q^75 + 11 * q^79 + 43 * q^81 - 33 * q^83 - 13 * q^85 + 30 * q^87 - 34 * q^89 - 12 * q^93 + 37 * q^95 - 17 * q^97 - 49 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	0	0
$2$	0	0
$3$	−0.852282	−0.492065	−0.246033	−	0.969262i	$-0.579127\pi$
$3$	−0.852282	−0.492065	−0.246033	+	0.969262i	$0.579127\pi$
$4$	0	0
$5$	−1.25440	−0.560983	−0.280492	−	0.959856i	$-0.590497\pi$
$5$	−1.25440	−0.560983	−0.280492	+	0.959856i	$0.590497\pi$
$6$	0	0
$7$	0	0
$7$	0	0
$8$	0	0
$9$	−2.27361	−0.757872
$10$	0	0
$11$	5.69315	1.71655	0.858275	−	0.513190i	$-0.171536\pi$
$11$	5.69315	1.71655	0.858275	+	0.513190i	$0.171536\pi$
$12$	0	0
$13$	1.56428	0.433852	0.216926	−	0.976188i	$-0.430397\pi$
$13$	1.56428	0.433852	0.216926	+	0.976188i	$0.430397\pi$
$14$	0	0
$15$	1.06910	0.276040
$16$	0	0
$17$	3.66751	0.889502	0.444751	−	0.895654i	$-0.353292\pi$
$17$	3.66751	0.889502	0.444751	+	0.895654i	$0.353292\pi$
$18$	0	0
$19$	−5.11241	−1.17287	−0.586434	−	0.809997i	$-0.699469\pi$
$19$	−5.11241	−1.17287	−0.586434	+	0.809997i	$0.699469\pi$
$20$	0	0
$21$	0	0
$22$	0	0
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	0	0
$25$	−3.42649	−0.685298
$26$	0	0
$27$	4.49461	0.864988
$28$	0	0
$29$	−3.12094	−0.579544	−0.289772	−	0.957096i	$-0.593579\pi$
$29$	−3.12094	−0.579544	−0.289772	+	0.957096i	$0.593579\pi$
$30$	0	0
$31$	−1.41394	−0.253951	−0.126975	−	0.991906i	$-0.540527\pi$
$31$	−1.41394	−0.253951	−0.126975	+	0.991906i	$0.540527\pi$
$32$	0	0
$33$	−4.85217	−0.844655
$34$	0	0
$35$	0	0
$36$	0	0
$37$	1.30698	0.214866	0.107433	−	0.994212i	$-0.465737\pi$
$37$	1.30698	0.214866	0.107433	+	0.994212i	$0.465737\pi$
$38$	0	0
$39$	−1.33321	−0.213484
$40$	0	0
$41$	2.24298	0.350295	0.175148	−	0.984542i	$-0.443960\pi$
$41$	2.24298	0.350295	0.175148	+	0.984542i	$0.443960\pi$
$42$	0	0
$43$	−5.84516	−0.891378	−0.445689	−	0.895188i	$-0.647041\pi$
$43$	−5.84516	−0.891378	−0.445689	+	0.895188i	$0.647041\pi$
$44$	0	0
$45$	2.85201	0.425153
$46$	0	0
$47$	−4.61410	−0.673036	−0.336518	−	0.941677i	$-0.609249\pi$
$47$	−4.61410	−0.673036	−0.336518	+	0.941677i	$0.609249\pi$
$48$	0	0
$49$	0	0
$50$	0	0
$51$	−3.12575	−0.437693
$52$	0	0
$53$	8.59490	1.18060	0.590300	−	0.807184i	$-0.299009\pi$
$53$	8.59490	1.18060	0.590300	+	0.807184i	$0.299009\pi$
$54$	0	0
$55$	−7.14147	−0.962956
$56$	0	0
$57$	4.35722	0.577128
$58$	0	0
$59$	−12.9000	−1.67944	−0.839719	−	0.543021i	$-0.817280\pi$
$59$	−12.9000	−1.67944	−0.839719	+	0.543021i	$0.817280\pi$
$60$	0	0
$61$	−5.04838	−0.646379	−0.323189	−	0.946334i	$-0.604755\pi$
$61$	−5.04838	−0.646379	−0.323189	+	0.946334i	$0.604755\pi$
$62$	0	0
$63$	0	0
$64$	0	0
$65$	−1.96222	−0.243384
$66$	0	0
$67$	12.7962	1.56330	0.781650	−	0.623717i	$-0.214378\pi$
$67$	12.7962	1.56330	0.781650	+	0.623717i	$0.214378\pi$
$68$	0	0
$69$	0.852282	0.102603
$70$	0	0
$71$	12.6302	1.49893	0.749463	−	0.662047i	$-0.230312\pi$
$71$	12.6302	1.49893	0.749463	+	0.662047i	$0.230312\pi$
$72$	0	0
$73$	−9.46838	−1.10819	−0.554095	−	0.832453i	$-0.686936\pi$
$73$	−9.46838	−1.10819	−0.554095	+	0.832453i	$0.686936\pi$
$74$	0	0
$75$	2.92034	0.337211
$76$	0	0
$77$	0	0
$78$	0	0
$79$	6.31953	0.711003	0.355501	−	0.934676i	$-0.384310\pi$
$79$	6.31953	0.711003	0.355501	+	0.934676i	$0.384310\pi$
$80$	0	0
$81$	2.99017	0.332241
$82$	0	0
$83$	−11.3499	−1.24581	−0.622906	−	0.782297i	$-0.714048\pi$
$83$	−11.3499	−1.24581	−0.622906	+	0.782297i	$0.714048\pi$
$84$	0	0
$85$	−4.60051	−0.498996
$86$	0	0
$87$	2.65992	0.285173
$88$	0	0
$89$	−1.76876	−0.187488	−0.0937441	−	0.995596i	$-0.529884\pi$
$89$	−1.76876	−0.187488	−0.0937441	+	0.995596i	$0.529884\pi$
$90$	0	0
$91$	0	0
$92$	0	0
$93$	1.20507	0.124960
$94$	0	0
$95$	6.41299	0.657959
$96$	0	0
$97$	6.92877	0.703510	0.351755	−	0.936092i	$-0.385585\pi$
$97$	6.92877	0.703510	0.351755	+	0.936092i	$0.385585\pi$
$98$	0	0
$99$	−12.9440	−1.30092
$100$	0	0
$101$	12.6875	1.26246	0.631228	−	0.775597i	$-0.282551\pi$
$101$	12.6875	1.26246	0.631228	+	0.775597i	$0.282551\pi$
$102$	0	0
$103$	−7.64083	−0.752873	−0.376437	−	0.926442i	$-0.622851\pi$
$103$	−7.64083	−0.752873	−0.376437	+	0.926442i	$0.622851\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	5.39540	0.521593	0.260796	−	0.965394i	$-0.416015\pi$
$107$	5.39540	0.521593	0.260796	+	0.965394i	$0.416015\pi$
$108$	0	0
$109$	−4.47188	−0.428328	−0.214164	−	0.976798i	$-0.568703\pi$
$109$	−4.47188	−0.428328	−0.214164	+	0.976798i	$0.568703\pi$
$110$	0	0
$111$	−1.11392	−0.105728
$112$	0	0
$113$	−2.08084	−0.195749	−0.0978745	−	0.995199i	$-0.531204\pi$
$113$	−2.08084	−0.195749	−0.0978745	+	0.995199i	$0.531204\pi$
$114$	0	0
$115$	1.25440	0.116973
$116$	0	0
$117$	−3.55656	−0.328804
$118$	0	0
$119$	0	0
$120$	0	0
$121$	21.4120	1.94654
$122$	0	0
$123$	−1.91166	−0.172368
$124$	0	0
$125$	10.5702	0.945424
$126$	0	0
$127$	−8.74889	−0.776339	−0.388169	−	0.921588i	$-0.626892\pi$
$127$	−8.74889	−0.776339	−0.388169	+	0.921588i	$0.626892\pi$
$128$	0	0
$129$	4.98172	0.438616
$130$	0	0
$131$	18.7683	1.63979	0.819895	−	0.572514i	$-0.194032\pi$
$131$	18.7683	1.63979	0.819895	+	0.572514i	$0.194032\pi$
$132$	0	0
$133$	0	0
$134$	0	0
$135$	−5.63802	−0.485244
$136$	0	0
$137$	−7.42221	−0.634122	−0.317061	−	0.948405i	$-0.602696\pi$
$137$	−7.42221	−0.634122	−0.317061	+	0.948405i	$0.602696\pi$
$138$	0	0
$139$	−7.40666	−0.628225	−0.314112	−	0.949386i	$-0.601707\pi$
$139$	−7.40666	−0.628225	−0.314112	+	0.949386i	$0.601707\pi$
$140$	0	0
$141$	3.93251	0.331178
$142$	0	0
$143$	8.90567	0.744729
$144$	0	0
$145$	3.91489	0.325114
$146$	0	0
$147$	0	0
$148$	0	0
$149$	−8.47668	−0.694436	−0.347218	−	0.937784i	$-0.612874\pi$
$149$	−8.47668	−0.694436	−0.347218	+	0.937784i	$0.612874\pi$
$150$	0	0
$151$	10.4980	0.854315	0.427158	−	0.904177i	$-0.359515\pi$
$151$	10.4980	0.854315	0.427158	+	0.904177i	$0.359515\pi$
$152$	0	0
$153$	−8.33851	−0.674128
$154$	0	0
$155$	1.77364	0.142462
$156$	0	0
$157$	−10.1234	−0.807934	−0.403967	−	0.914773i	$-0.632369\pi$
$157$	−10.1234	−0.807934	−0.403967	+	0.914773i	$0.632369\pi$
$158$	0	0
$159$	−7.32528	−0.580932
$160$	0	0
$161$	0	0
$162$	0	0
$163$	4.73578	0.370935	0.185468	−	0.982650i	$-0.440620\pi$
$163$	4.73578	0.370935	0.185468	+	0.982650i	$0.440620\pi$
$164$	0	0
$165$	6.08655	0.473837
$166$	0	0
$167$	−20.1367	−1.55822	−0.779110	−	0.626887i	$-0.784329\pi$
$167$	−20.1367	−1.55822	−0.779110	+	0.626887i	$0.784329\pi$
$168$	0	0
$169$	−10.5530	−0.811772
$170$	0	0
$171$	11.6237	0.888883
$172$	0	0
$173$	3.30436	0.251226	0.125613	−	0.992079i	$-0.459910\pi$
$173$	3.30436	0.251226	0.125613	+	0.992079i	$0.459910\pi$
$174$	0	0
$175$	0	0
$176$	0	0
$177$	10.9944	0.826393
$178$	0	0
$179$	16.4997	1.23324	0.616622	−	0.787259i	$-0.288501\pi$
$179$	16.4997	1.23324	0.616622	+	0.787259i	$0.288501\pi$
$180$	0	0
$181$	−11.8233	−0.878820	−0.439410	−	0.898287i	$-0.644812\pi$
$181$	−11.8233	−0.878820	−0.439410	+	0.898287i	$0.644812\pi$
$182$	0	0
$183$	4.30265	0.318061
$184$	0	0
$185$	−1.63947	−0.120536
$186$	0	0
$187$	20.8797	1.52687
$188$	0	0
$189$	0	0
$190$	0	0
$191$	−12.0118	−0.869147	−0.434573	−	0.900636i	$-0.643101\pi$
$191$	−12.0118	−0.869147	−0.434573	+	0.900636i	$0.643101\pi$
$192$	0	0
$193$	5.81516	0.418585	0.209292	−	0.977853i	$-0.432884\pi$
$193$	5.81516	0.418585	0.209292	+	0.977853i	$0.432884\pi$
$194$	0	0
$195$	1.67237	0.119761
$196$	0	0
$197$	10.5460	0.751371	0.375686	−	0.926747i	$-0.377407\pi$
$197$	10.5460	0.751371	0.375686	+	0.926747i	$0.377407\pi$
$198$	0	0
$199$	8.12482	0.575954	0.287977	−	0.957637i	$-0.407017\pi$
$199$	8.12482	0.575954	0.287977	+	0.957637i	$0.407017\pi$
$200$	0	0
$201$	−10.9059	−0.769246
$202$	0	0
$203$	0	0
$204$	0	0
$205$	−2.81359	−0.196510
$206$	0	0
$207$	2.27361	0.158027
$208$	0	0
$209$	−29.1057	−2.01329
$210$	0	0
$211$	−20.3208	−1.39894	−0.699470	−	0.714662i	$-0.746581\pi$
$211$	−20.3208	−1.39894	−0.699470	+	0.714662i	$0.746581\pi$
$212$	0	0
$213$	−10.7645	−0.737569
$214$	0	0
$215$	7.33215	0.500048
$216$	0	0
$217$	0	0
$218$	0	0
$219$	8.06973	0.545302
$220$	0	0
$221$	5.73700	0.385912
$222$	0	0
$223$	−16.9855	−1.13743	−0.568716	−	0.822534i	$-0.692560\pi$
$223$	−16.9855	−1.13743	−0.568716	+	0.822534i	$0.692560\pi$
$224$	0	0
$225$	7.79052	0.519368
$226$	0	0
$227$	14.0534	0.932755	0.466377	−	0.884586i	$-0.345559\pi$
$227$	14.0534	0.932755	0.466377	+	0.884586i	$0.345559\pi$
$228$	0	0
$229$	−0.887118	−0.0586224	−0.0293112	−	0.999570i	$-0.509331\pi$
$229$	−0.887118	−0.0586224	−0.0293112	+	0.999570i	$0.509331\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	−15.5956	−1.02170	−0.510849	−	0.859670i	$-0.670669\pi$
$233$	−15.5956	−1.02170	−0.510849	+	0.859670i	$0.670669\pi$
$234$	0	0
$235$	5.78791	0.377562
$236$	0	0
$237$	−5.38602	−0.349860
$238$	0	0
$239$	−6.73697	−0.435778	−0.217889	−	0.975974i	$-0.569917\pi$
$239$	−6.73697	−0.435778	−0.217889	+	0.975974i	$0.569917\pi$
$240$	0	0
$241$	−23.0886	−1.48727	−0.743635	−	0.668586i	$-0.766900\pi$
$241$	−23.0886	−1.48727	−0.743635	+	0.668586i	$0.766900\pi$
$242$	0	0
$243$	−16.0323	−1.02847
$244$	0	0
$245$	0	0
$246$	0	0
$247$	−7.99723	−0.508851
$248$	0	0
$249$	9.67331	0.613021
$250$	0	0
$251$	27.6053	1.74243	0.871215	−	0.490901i	$-0.163332\pi$
$251$	27.6053	1.74243	0.871215	+	0.490901i	$0.163332\pi$
$252$	0	0
$253$	−5.69315	−0.357925
$254$	0	0
$255$	3.92093	0.245538
$256$	0	0
$257$	−10.1877	−0.635489	−0.317744	−	0.948176i	$-0.602925\pi$
$257$	−10.1877	−0.635489	−0.317744	+	0.948176i	$0.602925\pi$
$258$	0	0
$259$	0	0
$260$	0	0
$261$	7.09581	0.439220
$262$	0	0
$263$	13.6935	0.844378	0.422189	−	0.906508i	$-0.361262\pi$
$263$	13.6935	0.844378	0.422189	+	0.906508i	$0.361262\pi$
$264$	0	0
$265$	−10.7814	−0.662297
$266$	0	0
$267$	1.50748	0.0922565
$268$	0	0
$269$	−22.2932	−1.35924	−0.679621	−	0.733563i	$-0.737856\pi$
$269$	−22.2932	−1.35924	−0.679621	+	0.733563i	$0.737856\pi$
$270$	0	0
$271$	5.60415	0.340428	0.170214	−	0.985407i	$-0.445554\pi$
$271$	5.60415	0.340428	0.170214	+	0.985407i	$0.445554\pi$
$272$	0	0
$273$	0	0
$274$	0	0
$275$	−19.5075	−1.17635
$276$	0	0
$277$	−20.6574	−1.24118	−0.620592	−	0.784133i	$-0.713108\pi$
$277$	−20.6574	−1.24118	−0.620592	+	0.784133i	$0.713108\pi$
$278$	0	0
$279$	3.21475	0.192462
$280$	0	0
$281$	28.5499	1.70314	0.851572	−	0.524238i	$-0.175650\pi$
$281$	28.5499	1.70314	0.851572	+	0.524238i	$0.175650\pi$
$282$	0	0
$283$	8.89908	0.528996	0.264498	−	0.964386i	$-0.414794\pi$
$283$	8.89908	0.528996	0.264498	+	0.964386i	$0.414794\pi$
$284$	0	0
$285$	−5.46568	−0.323759
$286$	0	0
$287$	0	0
$288$	0	0
$289$	−3.54937	−0.208786
$290$	0	0
$291$	−5.90527	−0.346173
$292$	0	0
$293$	−7.85210	−0.458725	−0.229362	−	0.973341i	$-0.573664\pi$
$293$	−7.85210	−0.458725	−0.229362	+	0.973341i	$0.573664\pi$
$294$	0	0
$295$	16.1817	0.942136
$296$	0	0
$297$	25.5885	1.48479
$298$	0	0
$299$	−1.56428	−0.0904645
$300$	0	0
$301$	0	0
$302$	0	0
$303$	−10.8134	−0.621211
$304$	0	0
$305$	6.33267	0.362608
$306$	0	0
$307$	−11.7088	−0.668258	−0.334129	−	0.942527i	$-0.608442\pi$
$307$	−11.7088	−0.668258	−0.334129	+	0.942527i	$0.608442\pi$
$308$	0	0
$309$	6.51214	0.370463
$310$	0	0
$311$	−31.5492	−1.78899	−0.894497	−	0.447075i	$-0.852466\pi$
$311$	−31.5492	−1.78899	−0.894497	+	0.447075i	$0.852466\pi$
$312$	0	0
$313$	14.4850	0.818738	0.409369	−	0.912369i	$-0.365749\pi$
$313$	14.4850	0.818738	0.409369	+	0.912369i	$0.365749\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	−20.2571	−1.13775	−0.568877	−	0.822423i	$-0.692622\pi$
$317$	−20.2571	−1.13775	−0.568877	+	0.822423i	$0.692622\pi$
$318$	0	0
$319$	−17.7680	−0.994816
$320$	0	0
$321$	−4.59840	−0.256658
$322$	0	0
$323$	−18.7498	−1.04327
$324$	0	0
$325$	−5.35998	−0.297318
$326$	0	0
$327$	3.81130	0.210765
$328$	0	0
$329$	0	0
$330$	0	0
$331$	−4.99399	−0.274495	−0.137247	−	0.990537i	$-0.543826\pi$
$331$	−4.99399	−0.274495	−0.137247	+	0.990537i	$0.543826\pi$
$332$	0	0
$333$	−2.97157	−0.162841
$334$	0	0
$335$	−16.0515	−0.876985
$336$	0	0
$337$	−13.8245	−0.753070	−0.376535	−	0.926402i	$-0.622885\pi$
$337$	−13.8245	−0.753070	−0.376535	+	0.926402i	$0.622885\pi$
$338$	0	0
$339$	1.77346	0.0963213
$340$	0	0
$341$	−8.04976	−0.435919
$342$	0	0
$343$	0	0
$344$	0	0
$345$	−1.06910	−0.0575584
$346$	0	0
$347$	−15.3718	−0.825201	−0.412601	−	0.910912i	$-0.635379\pi$
$347$	−15.3718	−0.825201	−0.412601	+	0.910912i	$0.635379\pi$
$348$	0	0
$349$	−33.3719	−1.78636	−0.893178	−	0.449703i	$-0.851530\pi$
$349$	−33.3719	−1.78636	−0.893178	+	0.449703i	$0.851530\pi$
$350$	0	0
$351$	7.03081	0.375277
$352$	0	0
$353$	−4.31647	−0.229743	−0.114871	−	0.993380i	$-0.536646\pi$
$353$	−4.31647	−0.229743	−0.114871	+	0.993380i	$0.536646\pi$
$354$	0	0
$355$	−15.8432	−0.840872
$356$	0	0
$357$	0	0
$358$	0	0
$359$	−13.5651	−0.715941	−0.357970	−	0.933733i	$-0.616531\pi$
$359$	−13.5651	−0.715941	−0.357970	+	0.933733i	$0.616531\pi$
$360$	0	0
$361$	7.13676	0.375619
$362$	0	0
$363$	−18.2491	−0.957827
$364$	0	0
$365$	11.8771	0.621676
$366$	0	0
$367$	13.0604	0.681745	0.340872	−	0.940110i	$-0.389278\pi$
$367$	13.0604	0.681745	0.340872	+	0.940110i	$0.389278\pi$
$368$	0	0
$369$	−5.09968	−0.265479
$370$	0	0
$371$	0	0
$372$	0	0
$373$	3.04346	0.157584	0.0787922	−	0.996891i	$-0.474894\pi$
$373$	3.04346	0.157584	0.0787922	+	0.996891i	$0.474894\pi$
$374$	0	0
$375$	−9.00876	−0.465210
$376$	0	0
$377$	−4.88201	−0.251436
$378$	0	0
$379$	−17.4799	−0.897882	−0.448941	−	0.893561i	$-0.648199\pi$
$379$	−17.4799	−0.897882	−0.448941	+	0.893561i	$0.648199\pi$
$380$	0	0
$381$	7.45653	0.382009
$382$	0	0
$383$	−24.1527	−1.23415	−0.617074	−	0.786905i	$-0.711682\pi$
$383$	−24.1527	−1.23415	−0.617074	+	0.786905i	$0.711682\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	13.2896	0.675550
$388$	0	0
$389$	−8.57089	−0.434561	−0.217281	−	0.976109i	$-0.569719\pi$
$389$	−8.57089	−0.434561	−0.217281	+	0.976109i	$0.569719\pi$
$390$	0	0
$391$	−3.66751	−0.185474
$392$	0	0
$393$	−15.9959	−0.806884
$394$	0	0
$395$	−7.92719	−0.398860
$396$	0	0
$397$	−29.0201	−1.45648	−0.728238	−	0.685324i	$-0.759661\pi$
$397$	−29.0201	−1.45648	−0.728238	+	0.685324i	$0.759661\pi$
$398$	0	0
$399$	0	0
$400$	0	0
$401$	15.4136	0.769719	0.384860	−	0.922975i	$-0.374250\pi$
$401$	15.4136	0.769719	0.384860	+	0.922975i	$0.374250\pi$
$402$	0	0
$403$	−2.21179	−0.110177
$404$	0	0
$405$	−3.75086	−0.186382
$406$	0	0
$407$	7.44085	0.368829
$408$	0	0
$409$	−30.0942	−1.48806	−0.744031	−	0.668145i	$-0.767089\pi$
$409$	−30.0942	−1.48806	−0.744031	+	0.668145i	$0.767089\pi$
$410$	0	0
$411$	6.32582	0.312030
$412$	0	0
$413$	0	0
$414$	0	0
$415$	14.2373	0.698880
$416$	0	0
$417$	6.31257	0.309128
$418$	0	0
$419$	10.0662	0.491765	0.245883	−	0.969300i	$-0.420922\pi$
$419$	10.0662	0.491765	0.245883	+	0.969300i	$0.420922\pi$
$420$	0	0
$421$	−7.32442	−0.356970	−0.178485	−	0.983943i	$-0.557120\pi$
$421$	−7.32442	−0.356970	−0.178485	+	0.983943i	$0.557120\pi$
$422$	0	0
$423$	10.4907	0.510075
$424$	0	0
$425$	−12.5667	−0.609574
$426$	0	0
$427$	0	0
$428$	0	0
$429$	−7.59014	−0.366456
$430$	0	0
$431$	36.1798	1.74272	0.871360	−	0.490645i	$-0.163239\pi$
$431$	36.1798	1.74272	0.871360	+	0.490645i	$0.163239\pi$
$432$	0	0
$433$	−10.8417	−0.521017	−0.260508	−	0.965472i	$-0.583890\pi$
$433$	−10.8417	−0.521017	−0.260508	+	0.965472i	$0.583890\pi$
$434$	0	0
$435$	−3.33660	−0.159977
$436$	0	0
$437$	5.11241	0.244560
$438$	0	0
$439$	−1.75061	−0.0835522	−0.0417761	−	0.999127i	$-0.513302\pi$
$439$	−1.75061	−0.0835522	−0.0417761	+	0.999127i	$0.513302\pi$
$440$	0	0
$441$	0	0
$442$	0	0
$443$	−33.6297	−1.59780	−0.798898	−	0.601467i	$-0.794583\pi$
$443$	−33.6297	−1.59780	−0.798898	+	0.601467i	$0.794583\pi$
$444$	0	0
$445$	2.21873	0.105178
$446$	0	0
$447$	7.22452	0.341708
$448$	0	0
$449$	17.9122	0.845331	0.422666	−	0.906286i	$-0.361094\pi$
$449$	17.9122	0.845331	0.422666	+	0.906286i	$0.361094\pi$
$450$	0	0
$451$	12.7697	0.601299
$452$	0	0
$453$	−8.94726	−0.420379
$454$	0	0
$455$	0	0
$456$	0	0
$457$	−27.6600	−1.29388	−0.646940	−	0.762541i	$-0.723952\pi$
$457$	−27.6600	−1.29388	−0.646940	+	0.762541i	$0.723952\pi$
$458$	0	0
$459$	16.4840	0.769408
$460$	0	0
$461$	−22.2048	−1.03418	−0.517091	−	0.855930i	$-0.672985\pi$
$461$	−22.2048	−1.03418	−0.517091	+	0.855930i	$0.672985\pi$
$462$	0	0
$463$	40.9791	1.90446	0.952230	−	0.305382i	$-0.0987840\pi$
$463$	40.9791	1.90446	0.952230	+	0.305382i	$0.0987840\pi$
$464$	0	0
$465$	−1.51164	−0.0701006
$466$	0	0
$467$	−7.80199	−0.361033	−0.180516	−	0.983572i	$-0.557777\pi$
$467$	−7.80199	−0.361033	−0.180516	+	0.983572i	$0.557777\pi$
$468$	0	0
$469$	0	0
$470$	0	0
$471$	8.62798	0.397557
$472$	0	0
$473$	−33.2774	−1.53010
$474$	0	0
$475$	17.5176	0.803764
$476$	0	0
$477$	−19.5415	−0.894743
$478$	0	0
$479$	17.8951	0.817650	0.408825	−	0.912613i	$-0.365939\pi$
$479$	17.8951	0.817650	0.408825	+	0.912613i	$0.365939\pi$
$480$	0	0
$481$	2.04448	0.0932203
$482$	0	0
$483$	0	0
$484$	0	0
$485$	−8.69142	−0.394657
$486$	0	0
$487$	−33.5735	−1.52136	−0.760681	−	0.649126i	$-0.775135\pi$
$487$	−33.5735	−1.52136	−0.760681	+	0.649126i	$0.775135\pi$
$488$	0	0
$489$	−4.03622	−0.182524
$490$	0	0
$491$	−28.5841	−1.28998	−0.644992	−	0.764190i	$-0.723139\pi$
$491$	−28.5841	−1.28998	−0.644992	+	0.764190i	$0.723139\pi$
$492$	0	0
$493$	−11.4461	−0.515505
$494$	0	0
$495$	16.2370	0.729797
$496$	0	0
$497$	0	0
$498$	0	0
$499$	42.3896	1.89762	0.948809	−	0.315849i	$-0.102289\pi$
$499$	42.3896	1.89762	0.948809	+	0.315849i	$0.102289\pi$
$500$	0	0
$501$	17.1621	0.766747
$502$	0	0
$503$	10.2991	0.459216	0.229608	−	0.973283i	$-0.426256\pi$
$503$	10.2991	0.459216	0.229608	+	0.973283i	$0.426256\pi$
$504$	0	0
$505$	−15.9152	−0.708217
$506$	0	0
$507$	8.99417	0.399445
$508$	0	0
$509$	3.75611	0.166487	0.0832434	−	0.996529i	$-0.473472\pi$
$509$	3.75611	0.166487	0.0832434	+	0.996529i	$0.473472\pi$
$510$	0	0
$511$	0	0
$512$	0	0
$513$	−22.9783	−1.01452
$514$	0	0
$515$	9.58463	0.422349
$516$	0	0
$517$	−26.2688	−1.15530
$518$	0	0
$519$	−2.81625	−0.123619
$520$	0	0
$521$	−19.3844	−0.849247	−0.424624	−	0.905370i	$-0.639594\pi$
$521$	−19.3844	−0.849247	−0.424624	+	0.905370i	$0.639594\pi$
$522$	0	0
$523$	4.41375	0.193000	0.0964998	−	0.995333i	$-0.469235\pi$
$523$	4.41375	0.193000	0.0964998	+	0.995333i	$0.469235\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	−5.18563	−0.225890
$528$	0	0
$529$	1.00000	0.0434783
$530$	0	0
$531$	29.3296	1.27280
$532$	0	0
$533$	3.50865	0.151976
$534$	0	0
$535$	−6.76797	−0.292605
$536$	0	0
$537$	−14.0624	−0.606837
$538$	0	0
$539$	0	0
$540$	0	0
$541$	−28.5071	−1.22562	−0.612809	−	0.790231i	$-0.709960\pi$
$541$	−28.5071	−1.22562	−0.612809	+	0.790231i	$0.709960\pi$
$542$	0	0
$543$	10.0768	0.432437
$544$	0	0
$545$	5.60951	0.240285
$546$	0	0
$547$	5.98857	0.256053	0.128026	−	0.991771i	$-0.459136\pi$
$547$	5.98857	0.256053	0.128026	+	0.991771i	$0.459136\pi$
$548$	0	0
$549$	11.4781	0.489872
$550$	0	0
$551$	15.9555	0.679728
$552$	0	0
$553$	0	0
$554$	0	0
$555$	1.39729	0.0593118
$556$	0	0
$557$	−20.9867	−0.889235	−0.444617	−	0.895721i	$-0.646660\pi$
$557$	−20.9867	−0.889235	−0.444617	+	0.895721i	$0.646660\pi$
$558$	0	0
$559$	−9.14345	−0.386727
$560$	0	0
$561$	−17.7954	−0.751322
$562$	0	0
$563$	−42.1535	−1.77656	−0.888279	−	0.459305i	$-0.848099\pi$
$563$	−42.1535	−1.77656	−0.888279	+	0.459305i	$0.848099\pi$
$564$	0	0
$565$	2.61020	0.109812
$566$	0	0
$567$	0	0
$568$	0	0
$569$	−27.2016	−1.14035	−0.570176	−	0.821522i	$-0.693125\pi$
$569$	−27.2016	−1.14035	−0.570176	+	0.821522i	$0.693125\pi$
$570$	0	0
$571$	39.5823	1.65647	0.828233	−	0.560383i	$-0.189346\pi$
$571$	39.5823	1.65647	0.828233	+	0.560383i	$0.189346\pi$
$572$	0	0
$573$	10.2375	0.427677
$574$	0	0
$575$	3.42649	0.142894
$576$	0	0
$577$	−21.7450	−0.905257	−0.452629	−	0.891699i	$-0.649514\pi$
$577$	−21.7450	−0.905257	−0.452629	+	0.891699i	$0.649514\pi$
$578$	0	0
$579$	−4.95616	−0.205971
$580$	0	0
$581$	0	0
$582$	0	0
$583$	48.9321	2.02656
$584$	0	0
$585$	4.46134	0.184454
$586$	0	0
$587$	11.8644	0.489695	0.244848	−	0.969562i	$-0.421262\pi$
$587$	11.8644	0.489695	0.244848	+	0.969562i	$0.421262\pi$
$588$	0	0
$589$	7.22863	0.297851
$590$	0	0
$591$	−8.98817	−0.369724
$592$	0	0
$593$	24.4598	1.00444	0.502222	−	0.864739i	$-0.332516\pi$
$593$	24.4598	1.00444	0.502222	+	0.864739i	$0.332516\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	−6.92464	−0.283407
$598$	0	0
$599$	39.9320	1.63158	0.815789	−	0.578349i	$-0.196303\pi$
$599$	39.9320	1.63158	0.815789	+	0.578349i	$0.196303\pi$
$600$	0	0
$601$	−3.52664	−0.143855	−0.0719273	−	0.997410i	$-0.522915\pi$
$601$	−3.52664	−0.143855	−0.0719273	+	0.997410i	$0.522915\pi$
$602$	0	0
$603$	−29.0936	−1.18478
$604$	0	0
$605$	−26.8591	−1.09198
$606$	0	0
$607$	12.2506	0.497236	0.248618	−	0.968602i	$-0.420024\pi$
$607$	12.2506	0.497236	0.248618	+	0.968602i	$0.420024\pi$
$608$	0	0
$609$	0	0
$610$	0	0
$611$	−7.21773	−0.291998
$612$	0	0
$613$	−7.99698	−0.322995	−0.161498	−	0.986873i	$-0.551632\pi$
$613$	−7.99698	−0.322995	−0.161498	+	0.986873i	$0.551632\pi$
$614$	0	0
$615$	2.39797	0.0966957
$616$	0	0
$617$	2.29366	0.0923394	0.0461697	−	0.998934i	$-0.485299\pi$
$617$	2.29366	0.0923394	0.0461697	+	0.998934i	$0.485299\pi$
$618$	0	0
$619$	44.2682	1.77929	0.889644	−	0.456655i	$-0.150953\pi$
$619$	44.2682	1.77929	0.889644	+	0.456655i	$0.150953\pi$
$620$	0	0
$621$	−4.49461	−0.180362
$622$	0	0
$623$	0	0
$624$	0	0
$625$	3.87328	0.154931
$626$	0	0
$627$	24.8063	0.990669
$628$	0	0
$629$	4.79337	0.191124
$630$	0	0
$631$	−25.6202	−1.01993	−0.509963	−	0.860196i	$-0.670341\pi$
$631$	−25.6202	−1.01993	−0.509963	+	0.860196i	$0.670341\pi$
$632$	0	0
$633$	17.3190	0.688370
$634$	0	0
$635$	10.9746	0.435513
$636$	0	0
$637$	0	0
$638$	0	0
$639$	−28.7161	−1.13599
$640$	0	0
$641$	26.6485	1.05255	0.526275	−	0.850314i	$-0.323588\pi$
$641$	26.6485	1.05255	0.526275	+	0.850314i	$0.323588\pi$
$642$	0	0
$643$	26.0623	1.02780	0.513899	−	0.857851i	$-0.328201\pi$
$643$	26.0623	1.02780	0.513899	+	0.857851i	$0.328201\pi$
$644$	0	0
$645$	−6.24906	−0.246056
$646$	0	0
$647$	26.3415	1.03559	0.517795	−	0.855504i	$-0.326753\pi$
$647$	26.3415	1.03559	0.517795	+	0.855504i	$0.326753\pi$
$648$	0	0
$649$	−73.4417	−2.88284
$650$	0	0
$651$	0	0
$652$	0	0
$653$	−37.8743	−1.48213	−0.741067	−	0.671431i	$-0.765680\pi$
$653$	−37.8743	−1.48213	−0.741067	+	0.671431i	$0.765680\pi$
$654$	0	0
$655$	−23.5428	−0.919895
$656$	0	0
$657$	21.5275	0.839866
$658$	0	0
$659$	−26.3762	−1.02747	−0.513735	−	0.857949i	$-0.671738\pi$
$659$	−26.3762	−1.02747	−0.513735	+	0.857949i	$0.671738\pi$
$660$	0	0
$661$	−7.08060	−0.275404	−0.137702	−	0.990474i	$-0.543972\pi$
$661$	−7.08060	−0.275404	−0.137702	+	0.990474i	$0.543972\pi$
$662$	0	0
$663$	−4.88955	−0.189894
$664$	0	0
$665$	0	0
$666$	0	0
$667$	3.12094	0.120843
$668$	0	0
$669$	14.4764	0.559691
$670$	0	0
$671$	−28.7412	−1.10954
$672$	0	0
$673$	48.1412	1.85571	0.927854	−	0.372945i	$-0.121652\pi$
$673$	48.1412	1.85571	0.927854	+	0.372945i	$0.121652\pi$
$674$	0	0
$675$	−15.4007	−0.592774
$676$	0	0
$677$	23.2831	0.894840	0.447420	−	0.894324i	$-0.352343\pi$
$677$	23.2831	0.894840	0.447420	+	0.894324i	$0.352343\pi$
$678$	0	0
$679$	0	0
$680$	0	0
$681$	−11.9774	−0.458976
$682$	0	0
$683$	−23.0087	−0.880403	−0.440201	−	0.897899i	$-0.645093\pi$
$683$	−23.0087	−0.880403	−0.440201	+	0.897899i	$0.645093\pi$
$684$	0	0
$685$	9.31040	0.355732
$686$	0	0
$687$	0.756075	0.0288461
$688$	0	0
$689$	13.4448	0.512206
$690$	0	0
$691$	−14.0399	−0.534102	−0.267051	−	0.963682i	$-0.586049\pi$
$691$	−14.0399	−0.534102	−0.267051	+	0.963682i	$0.586049\pi$
$692$	0	0
$693$	0	0
$694$	0	0
$695$	9.29089	0.352423
$696$	0	0
$697$	8.22617	0.311588
$698$	0	0
$699$	13.2918	0.502743
$700$	0	0
$701$	−47.3589	−1.78872	−0.894360	−	0.447348i	$-0.852369\pi$
$701$	−47.3589	−1.78872	−0.894360	+	0.447348i	$0.852369\pi$
$702$	0	0
$703$	−6.68183	−0.252010
$704$	0	0
$705$	−4.93293	−0.185785
$706$	0	0
$707$	0	0
$708$	0	0
$709$	−1.78461	−0.0670223	−0.0335111	−	0.999438i	$-0.510669\pi$
$709$	−1.78461	−0.0670223	−0.0335111	+	0.999438i	$0.510669\pi$
$710$	0	0
$711$	−14.3682	−0.538849
$712$	0	0
$713$	1.41394	0.0529524
$714$	0	0
$715$	−11.1712	−0.417781
$716$	0	0
$717$	5.74180	0.214431
$718$	0	0
$719$	−20.2776	−0.756225	−0.378113	−	0.925760i	$-0.623427\pi$
$719$	−20.2776	−0.756225	−0.378113	+	0.925760i	$0.623427\pi$
$720$	0	0
$721$	0	0
$722$	0	0
$723$	19.6780	0.731834
$724$	0	0
$725$	10.6939	0.397160
$726$	0	0
$727$	21.6753	0.803891	0.401945	−	0.915664i	$-0.368334\pi$
$727$	21.6753	0.803891	0.401945	+	0.915664i	$0.368334\pi$
$728$	0	0
$729$	4.69353	0.173835
$730$	0	0
$731$	−21.4372	−0.792883
$732$	0	0
$733$	−6.16020	−0.227532	−0.113766	−	0.993508i	$-0.536291\pi$
$733$	−6.16020	−0.227532	−0.113766	+	0.993508i	$0.536291\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	72.8505	2.68348
$738$	0	0
$739$	20.4283	0.751469	0.375734	−	0.926727i	$-0.377390\pi$
$739$	20.4283	0.751469	0.375734	+	0.926727i	$0.377390\pi$
$740$	0	0
$741$	6.81590	0.250388
$742$	0	0
$743$	−25.8822	−0.949527	−0.474763	−	0.880114i	$-0.657466\pi$
$743$	−25.8822	−0.949527	−0.474763	+	0.880114i	$0.657466\pi$
$744$	0	0
$745$	10.6331	0.389567
$746$	0	0
$747$	25.8053	0.944166
$748$	0	0
$749$	0	0
$750$	0	0
$751$	30.8444	1.12553	0.562765	−	0.826617i	$-0.309738\pi$
$751$	30.8444	1.12553	0.562765	+	0.826617i	$0.309738\pi$
$752$	0	0
$753$	−23.5275	−0.857390
$754$	0	0
$755$	−13.1687	−0.479256
$756$	0	0
$757$	35.3275	1.28400	0.641999	−	0.766705i	$-0.278105\pi$
$757$	35.3275	1.28400	0.641999	+	0.766705i	$0.278105\pi$
$758$	0	0
$759$	4.85217	0.176123
$760$	0	0
$761$	−14.4727	−0.524634	−0.262317	−	0.964982i	$-0.584487\pi$
$761$	−14.4727	−0.524634	−0.262317	+	0.964982i	$0.584487\pi$
$762$	0	0
$763$	0	0
$764$	0	0
$765$	10.4598	0.378175
$766$	0	0
$767$	−20.1792	−0.728628
$768$	0	0
$769$	51.7723	1.86696	0.933478	−	0.358634i	$-0.116757\pi$
$769$	51.7723	1.86696	0.933478	+	0.358634i	$0.116757\pi$
$770$	0	0
$771$	8.68276	0.312702
$772$	0	0
$773$	−9.21000	−0.331261	−0.165630	−	0.986188i	$-0.552966\pi$
$773$	−9.21000	−0.331261	−0.165630	+	0.986188i	$0.552966\pi$
$774$	0	0
$775$	4.84484	0.174032
$776$	0	0
$777$	0	0
$778$	0	0
$779$	−11.4671	−0.410850
$780$	0	0
$781$	71.9055	2.57298
$782$	0	0
$783$	−14.0274	−0.501298
$784$	0	0
$785$	12.6987	0.453238
$786$	0	0
$787$	−10.7550	−0.383376	−0.191688	−	0.981456i	$-0.561396\pi$
$787$	−10.7550	−0.383376	−0.191688	+	0.981456i	$0.561396\pi$
$788$	0	0
$789$	−11.6707	−0.415489
$790$	0	0
$791$	0	0
$792$	0	0
$793$	−7.89707	−0.280433
$794$	0	0
$795$	9.18880	0.325893
$796$	0	0
$797$	−26.1940	−0.927841	−0.463920	−	0.885877i	$-0.653558\pi$
$797$	−26.1940	−0.927841	−0.463920	+	0.885877i	$0.653558\pi$
$798$	0	0
$799$	−16.9223	−0.598666
$800$	0	0
$801$	4.02148	0.142092
$802$	0	0
$803$	−53.9049	−1.90226
$804$	0	0
$805$	0	0
$806$	0	0
$807$	19.0001	0.668836
$808$	0	0
$809$	−16.3267	−0.574017	−0.287009	−	0.957928i	$-0.592661\pi$
$809$	−16.3267	−0.574017	−0.287009	+	0.957928i	$0.592661\pi$
$810$	0	0
$811$	2.83871	0.0996805	0.0498403	−	0.998757i	$-0.484129\pi$
$811$	2.83871	0.0996805	0.0498403	+	0.998757i	$0.484129\pi$
$812$	0	0
$813$	−4.77632	−0.167513
$814$	0	0
$815$	−5.94055	−0.208088
$816$	0	0
$817$	29.8829	1.04547
$818$	0	0
$819$	0	0
$820$	0	0
$821$	−18.1508	−0.633469	−0.316734	−	0.948514i	$-0.602586\pi$
$821$	−18.1508	−0.633469	−0.316734	+	0.948514i	$0.602586\pi$
$822$	0	0
$823$	55.3849	1.93060	0.965299	−	0.261149i	$-0.0841014\pi$
$823$	55.3849	1.93060	0.965299	+	0.261149i	$0.0841014\pi$
$824$	0	0
$825$	16.6259	0.578840
$826$	0	0
$827$	35.4033	1.23109	0.615546	−	0.788101i	$-0.288935\pi$
$827$	35.4033	1.23109	0.615546	+	0.788101i	$0.288935\pi$
$828$	0	0
$829$	−29.9285	−1.03946	−0.519730	−	0.854331i	$-0.673967\pi$
$829$	−29.9285	−1.03946	−0.519730	+	0.854331i	$0.673967\pi$
$830$	0	0
$831$	17.6060	0.610744
$832$	0	0
$833$	0	0
$834$	0	0
$835$	25.2593	0.874136
$836$	0	0
$837$	−6.35509	−0.219664
$838$	0	0
$839$	−50.4631	−1.74218	−0.871090	−	0.491123i	$-0.836587\pi$
$839$	−50.4631	−1.74218	−0.871090	+	0.491123i	$0.836587\pi$
$840$	0	0
$841$	−19.2597	−0.664129
$842$	0	0
$843$	−24.3326	−0.838058
$844$	0	0
$845$	13.2377	0.455390
$846$	0	0
$847$	0	0
$848$	0	0
$849$	−7.58453	−0.260300
$850$	0	0
$851$	−1.30698	−0.0448028
$852$	0	0
$853$	15.5762	0.533319	0.266659	−	0.963791i	$-0.414080\pi$
$853$	15.5762	0.533319	0.266659	+	0.963791i	$0.414080\pi$
$854$	0	0
$855$	−14.5807	−0.498649
$856$	0	0
$857$	53.3293	1.82169	0.910847	−	0.412744i	$-0.135430\pi$
$857$	53.3293	1.82169	0.910847	+	0.412744i	$0.135430\pi$
$858$	0	0
$859$	−28.9713	−0.988489	−0.494244	−	0.869323i	$-0.664555\pi$
$859$	−28.9713	−0.988489	−0.494244	+	0.869323i	$0.664555\pi$
$860$	0	0
$861$	0	0
$862$	0	0
$863$	−30.3078	−1.03169	−0.515844	−	0.856683i	$-0.672522\pi$
$863$	−30.3078	−1.03169	−0.515844	+	0.856683i	$0.672522\pi$
$864$	0	0
$865$	−4.14497	−0.140933
$866$	0	0
$867$	3.02506	0.102737
$868$	0	0
$869$	35.9780	1.22047
$870$	0	0
$871$	20.0167	0.678242
$872$	0	0
$873$	−15.7533	−0.533170
$874$	0	0
$875$	0	0
$876$	0	0
$877$	−56.1593	−1.89636	−0.948182	−	0.317727i	$-0.897080\pi$
$877$	−56.1593	−1.89636	−0.948182	+	0.317727i	$0.897080\pi$
$878$	0	0
$879$	6.69221	0.225722
$880$	0	0
$881$	13.9372	0.469555	0.234777	−	0.972049i	$-0.424564\pi$
$881$	13.9372	0.469555	0.234777	+	0.972049i	$0.424564\pi$
$882$	0	0
$883$	−18.4755	−0.621751	−0.310875	−	0.950451i	$-0.600622\pi$
$883$	−18.4755	−0.621751	−0.310875	+	0.950451i	$0.600622\pi$
$884$	0	0
$885$	−13.7914	−0.463593
$886$	0	0
$887$	38.2000	1.28263	0.641315	−	0.767277i	$-0.278389\pi$
$887$	38.2000	1.28263	0.641315	+	0.767277i	$0.278389\pi$
$888$	0	0
$889$	0	0
$890$	0	0
$891$	17.0235	0.570308
$892$	0	0
$893$	23.5892	0.789382
$894$	0	0
$895$	−20.6971	−0.691829
$896$	0	0
$897$	1.33321	0.0445144
$898$	0	0
$899$	4.41281	0.147175
$900$	0	0
$901$	31.5219	1.05015
$902$	0	0
$903$	0	0
$904$	0	0
$905$	14.8311	0.493003
$906$	0	0
$907$	−58.6784	−1.94838	−0.974192	−	0.225723i	$-0.927526\pi$
$907$	−58.6784	−1.94838	−0.974192	+	0.225723i	$0.927526\pi$
$908$	0	0
$909$	−28.8466	−0.956780
$910$	0	0
$911$	−40.3639	−1.33731	−0.668657	−	0.743571i	$-0.733131\pi$
$911$	−40.3639	−1.33731	−0.668657	+	0.743571i	$0.733131\pi$
$912$	0	0
$913$	−64.6167	−2.13850
$914$	0	0
$915$	−5.39722	−0.178427
$916$	0	0
$917$	0	0
$918$	0	0
$919$	−8.57292	−0.282795	−0.141397	−	0.989953i	$-0.545160\pi$
$919$	−8.57292	−0.282795	−0.141397	+	0.989953i	$0.545160\pi$
$920$	0	0
$921$	9.97922	0.328827
$922$	0	0
$923$	19.7571	0.650312
$924$	0	0
$925$	−4.47836	−0.147248
$926$	0	0
$927$	17.3723	0.570581
$928$	0	0
$929$	−34.3785	−1.12792	−0.563961	−	0.825801i	$-0.690723\pi$
$929$	−34.3785	−1.12792	−0.563961	+	0.825801i	$0.690723\pi$
$930$	0	0
$931$	0	0
$932$	0	0
$933$	26.8889	0.880302
$934$	0	0
$935$	−26.1914	−0.856551
$936$	0	0
$937$	44.6318	1.45806	0.729028	−	0.684483i	$-0.239972\pi$
$937$	44.6318	1.45806	0.729028	+	0.684483i	$0.239972\pi$
$938$	0	0
$939$	−12.3453	−0.402873
$940$	0	0
$941$	−10.8015	−0.352118	−0.176059	−	0.984380i	$-0.556335\pi$
$941$	−10.8015	−0.352118	−0.176059	+	0.984380i	$0.556335\pi$
$942$	0	0
$943$	−2.24298	−0.0730416
$944$	0	0
$945$	0	0
$946$	0	0
$947$	−11.3196	−0.367838	−0.183919	−	0.982941i	$-0.558878\pi$
$947$	−11.3196	−0.367838	−0.183919	+	0.982941i	$0.558878\pi$
$948$	0	0
$949$	−14.8112	−0.480791
$950$	0	0
$951$	17.2648	0.559850
$952$	0	0
$953$	14.6644	0.475025	0.237513	−	0.971384i	$-0.423668\pi$
$953$	14.6644	0.475025	0.237513	+	0.971384i	$0.423668\pi$
$954$	0	0
$955$	15.0676	0.487577
$956$	0	0
$957$	15.1433	0.489515
$958$	0	0
$959$	0	0
$960$	0	0
$961$	−29.0008	−0.935509
$962$	0	0
$963$	−12.2671	−0.395301
$964$	0	0
$965$	−7.29452	−0.234819
$966$	0	0
$967$	−12.0906	−0.388806	−0.194403	−	0.980922i	$-0.562277\pi$
$967$	−12.0906	−0.388806	−0.194403	+	0.980922i	$0.562277\pi$
$968$	0	0
$969$	15.9801	0.513356
$970$	0	0
$971$	11.8409	0.379993	0.189996	−	0.981785i	$-0.439152\pi$
$971$	11.8409	0.379993	0.189996	+	0.981785i	$0.439152\pi$
$972$	0	0
$973$	0	0
$974$	0	0
$975$	4.56822	0.146300
$976$	0	0
$977$	−24.5731	−0.786163	−0.393082	−	0.919504i	$-0.628591\pi$
$977$	−24.5731	−0.786163	−0.393082	+	0.919504i	$0.628591\pi$
$978$	0	0
$979$	−10.0698	−0.321833
$980$	0	0
$981$	10.1673	0.324618
$982$	0	0
$983$	−6.35586	−0.202721	−0.101360	−	0.994850i	$-0.532319\pi$
$983$	−6.35586	−0.202721	−0.101360	+	0.994850i	$0.532319\pi$
$984$	0	0
$985$	−13.2289	−0.421507
$986$	0	0
$987$	0	0
$988$	0	0
$989$	5.84516	0.185865
$990$	0	0
$991$	−22.7199	−0.721721	−0.360861	−	0.932620i	$-0.617517\pi$
$991$	−22.7199	−0.721721	−0.360861	+	0.932620i	$0.617517\pi$
$992$	0	0
$993$	4.25629	0.135069
$994$	0	0
$995$	−10.1918	−0.323100
$996$	0	0
$997$	42.8999	1.35865	0.679327	−	0.733836i	$-0.262272\pi$
$997$	42.8999	1.35865	0.679327	+	0.733836i	$0.262272\pi$
$998$	0	0
$999$	5.87437	0.185857

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9016.2.a.bo.1.5		11
7.3	odd	6		1288.2.q.b.737.5	✓	22
7.5	odd	6		1288.2.q.b.921.5	yes	22
7.6	odd	2		9016.2.a.bn.1.7		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1288.2.q.b.737.5	✓	22	7.3	odd	6
1288.2.q.b.921.5	yes	22	7.5	odd	6
9016.2.a.bn.1.7		11	7.6	odd	2
9016.2.a.bo.1.5		11	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 9016 = 2^{3} \cdot 7^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9016.a (trivial)

\(f(q)\)	\(=\)	\(q-0.852282 q^{3} -1.25440 q^{5} -2.27361 q^{9} +O(q^{10})\)	\(q-0.852282 q^{3} -1.25440 q^{5} -2.27361 q^{9} +5.69315 q^{11} +1.56428 q^{13} +1.06910 q^{15} +3.66751 q^{17} -5.11241 q^{19} -1.00000 q^{23} -3.42649 q^{25} +4.49461 q^{27} -3.12094 q^{29} -1.41394 q^{31} -4.85217 q^{33} +1.30698 q^{37} -1.33321 q^{39} +2.24298 q^{41} -5.84516 q^{43} +2.85201 q^{45} -4.61410 q^{47} -3.12575 q^{51} +8.59490 q^{53} -7.14147 q^{55} +4.35722 q^{57} -12.9000 q^{59} -5.04838 q^{61} -1.96222 q^{65} +12.7962 q^{67} +0.852282 q^{69} +12.6302 q^{71} -9.46838 q^{73} +2.92034 q^{75} +6.31953 q^{79} +2.99017 q^{81} -11.3499 q^{83} -4.60051 q^{85} +2.65992 q^{87} -1.76876 q^{89} +1.20507 q^{93} +6.41299 q^{95} +6.92877 q^{97} -12.9440 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q + 2 q^{3} - 9 q^{5} + 11 q^{9}+O(q^{10}) \) 11 * q + 2 * q^3 - 9 * q^5 + 11 * q^9	\( 11 q + 2 q^{3} - 9 q^{5} + 11 q^{9} - 15 q^{13} - 2 q^{15} - 5 q^{17} - 11 q^{23} + 22 q^{25} + 5 q^{27} + 5 q^{29} - 6 q^{31} - 14 q^{33} - q^{37} + 11 q^{39} - 20 q^{41} - 7 q^{43} - 41 q^{45} + 3 q^{47} - 13 q^{51} + 19 q^{53} + 3 q^{55} - 5 q^{57} - 7 q^{59} - 39 q^{61} + 5 q^{65} + 7 q^{67} - 2 q^{69} - 19 q^{71} + 5 q^{73} - 16 q^{75} + 11 q^{79} + 43 q^{81} - 33 q^{83} - 13 q^{85} + 30 q^{87} - 34 q^{89} - 12 q^{93} + 37 q^{95} - 17 q^{97} - 49 q^{99}+O(q^{100}) \) 11 * q + 2 * q^3 - 9 * q^5 + 11 * q^9 - 15 * q^13 - 2 * q^15 - 5 * q^17 - 11 * q^23 + 22 * q^25 + 5 * q^27 + 5 * q^29 - 6 * q^31 - 14 * q^33 - q^37 + 11 * q^39 - 20 * q^41 - 7 * q^43 - 41 * q^45 + 3 * q^47 - 13 * q^51 + 19 * q^53 + 3 * q^55 - 5 * q^57 - 7 * q^59 - 39 * q^61 + 5 * q^65 + 7 * q^67 - 2 * q^69 - 19 * q^71 + 5 * q^73 - 16 * q^75 + 11 * q^79 + 43 * q^81 - 33 * q^83 - 13 * q^85 + 30 * q^87 - 34 * q^89 - 12 * q^93 + 37 * q^95 - 17 * q^97 - 49 * q^99

Introduction

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